1. Field of the Invention
This invention relates to a method and apparatus for nonlinear laser spectroscopy, and more particularly, to a method and apparatus using two or three input laser beams in a nonlinear four-wave mixing setup for ultrasensative analytical measurements of an analyte.
2. Description of Related Art
Research has taken place with regard to degenerate four-wave mixing (D4WM) techniques using a "backward-scattering" degenerate four-wave mixing (B-D4WM) optical setup for analytical measurements in discharge atomizers (see Tong, W. G., Chen, D. A., Appl. Spectrosc. 1987, 41, 586-590), flame atomizers (see Tong, W. G., Andrews, J. M., Wu, Z., Anal Chem. 1987, 59, 896-899), and room-temperature flow cells (see Wu, Z., Tong, W. G., Anal Chem. 1989, 61, 998-1001). In particular, the inventor of the present invention has described the use of B-D4WM to detect trace-concentrations of an analyte, such as eosin B dissolved in ethanol. In such an application of B-D4WM, two counter-propagating pump beams and a probe beam are mixed inside a nonlinear medium, and a phase-conjugate signal beam is generated via one of the four-wave mixing mechanisms. FIG. 1 illustrates the set-up used for detecting trace-concentrations in this manner. A laser beam 101 is generated by an argon ion laser. The laser beam is split by a first beam splitter 103, such that a first portion of the laser beam 101 forms the forward pump beam 107, and a second portion of the laser beam 101 forms the backward pump beam 109. The forward pump beam 107 is reflected by a reflector 111 which directs the forward bump beam toward an analyte cell 113. The analyte cell contains a volume of an analyte. The backward pump beam 109 is reflected by a second reflector 115 toward the analyte cell in the opposite direction from the forward pump beam 107. A portion 117 of the laser beam that passes through the first beam splitter 103 is reflected by the second beam splitter 105. The second portion of the laser beam is the probe beam 117. The probe beam 117 is reflected by the second beam splitter 105 through an amplitude modulation device 118 (such as a mechanical chopper), an aperture 120, a third beam splitter 123, and a lens 122, to a reflector 119. The reflector directs the beam 117 to the point in the analyte cell 113 to which both the forward pump beam and the backward pump beam 109 are directed. Generation of an optical phase conjugate beam 121 by D4WM in an absorbing liquid sample of an analyte contained within the analyte cell 113 results from formation of spatial gratings due to a thermally induced refractive index change in the nonlinear medium of the sample. The phase conjugate reflectivity can be described as: EQU R.ident.I.sub.s /I.sub.p =f.sup.2 Q.sup.2 I.sub.f I.sub.b exp(-.alpha.L)[1-exp(-.alpha.L/cos .THETA.)].sup.2 G(t.sub.D)
Where:
I.sub.s, i.sub.p, I.sub.f, and I.sub.b =the beam intensity of the conjugate signal beam 121, probe beam 117, forward pump beam 107, and backward pump beam 109, respectively; PA1 f=the fraction of absorbed light energy converted into heat, and is inversely proportional to the quantum efficiency of fluorescence of the analyte; PA1 .alpha.=the absorption coefficient; PA1 L=the sample path length; PA1 .THETA.=is the angle between the forward pump beam 107 and the probe beams 117; PA1 Q=[2n (dn/dt).sub.p ]/(.lambda..rho..sub.o C.sub.p); PA1 (dn/dt).sub.p =the change of refractive index due to temperature change at constant pressure, PA1 .rho..sub.0 =the equilibrium solvent density; PA1 C.sub.p =the specific heat at constant pressure,; PA1 .lambda.=the wavelength of the excitation laser source; PA1 G(t.sub.D)=thermal grating evolution and depends on the thermalization time and thermal diffusion time constant for the analyte molecules in the solution.
The above equation can be simplified to: EQU I.sub.s .about.Q.sup.2 I.sup.3 (.alpha.L/cos .THETA.).sup.2
by assuming that the absorption of the solution is small and the sample path length is short. Therefore, according to this formula, the intensity of the optical phase conjugate signal is proportional to the square of the absorption coefficient, and hence to the analyte concentration. Thus, by accurately measuring the intensity of the optical phase conjugate signal generated by incident light defracted off the spatial gratings generated in the sample in the analyte cell 113, the concentration of the analyte can be determined.
The signal beam 121 is transmitted back along the path of the input beam 117, and is reflected by the third beam splitter 123 toward an aperture 125, a filter 127, and a photomultiplier tube 129. The output of the photomultiplier tube is coupled to a lock-in amplifier 131, which filters out amplitude variations that occur at frequencies other than the frequency of the chopper 118 and out of phase with the chopper. The output of the lock-in amplifier 131 is then coupled to a computer 135 comprising an analog to digital converter. The computer 135 processes intensity information to determine the concentration of the analyte that was present in the sample cell 113.
This method for measuring concentrations has a detection limitation that makes it useful for detecting trace amounts of a substance, such as eosin B which is used in many areas, including protein labeling, and artificial food coloring. However, the amount of analyte that must be provided within the sample cell of such detectors is greater than is desireable in many circumstances. For example, when used with a capillary electrophoresis system, the laser beams are very difficult to focus within the very small confines of capillary tubes typically used. Furthermore, the physical set-up is difficult to align due to the fact that three beams which reflect off of five surfaces must be aligned to cause a phase conjugate signal to be generated. Furthermore, it would be desireable to reduce the laser power requirements and even further decrease the mass detection limitations of the system. Still further, it would be desirable for the laser probe volume to be reduced with shorter analyte absorption path length.
The present invention provides a method and apparatus which has lower mass detection limitations than the prior art, requires less laser power, is much easier to align, provides a means by which the laser beams used can be focused and mixed with a single lens within a sufficiently small area to allow detection directly within the capillary tube of a capillary electrophoresis system, and allows virtually any substance to be analyzed.